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JEE Advanced Mathematics question

MathematicsComplex NumbersJEE Advanced

Suppose are the vertices of an equilateral triangle inscribed in the circle . If and are in the clockwise sense then

Answer: (A)

Solution

The centre of the circle is the centroid, and the vertices are apart on . . Going clockwise, rotate by each time:

=2 cis(-)=2

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Question ID VK-108103